# Arithmetic and Geometric Sequences and Series 49 Objective

- Slides: 25

Arithmetic and Geometric Sequences and Series 4/9 Objective: Students will be able to understand arithmetic series and sequence. Students will be able to understand geometric series and sequence. EQ: How do I find a given term in an arithmetic or geometric sequence? How do I find the sum of an arithmetic or geometric series?

An introduction… Arithmetic Sequences ADD To get next term Arithmetic Series SUM of Terms Geometric Sequences MULTIPLY To get next term Geometric Series SUM of Terms

Arithmetic Sequences and Series

Find the next four terms of – 9, -2, 5, … Arithmetic Sequence ___ is the common difference (d) Common Difference (d) – what we ADD to get next term Find the next four terms: -3, -11, -19, __, __ What is the common difference?

Find the next four terms of 0, 7, 14, … Find the next four terms of x, 2 x, 3 x, … Find the next four terms of 5 k, -7 k, …

Find the next four terms of 0, 7, 14, … Find the next four terms of x, 2 x, 3 x, … Find the next four terms of 5 k, -7 k, …

Create an arithmetic sequence with at least 4 terms and d = -3

Vocabulary of Sequences (Universal)

Given an arithmetic sequence with

Given an arithmetic sequence with

Try this one: __ __ __

Try this one: __ __ __

Try this one: 1. 5 __ ? __ 16 __ __ 0. 5 __ an = a 1 + (n – 1)d an = 1. 5 + (16 – 1)(0. 5) an = 9

Find two arithmetic means between – 4 and 5 -4, ____, 5 The two arithmetic means are __ and __, since – 4, __, 5 forms an arithmetic sequence.

Find two arithmetic means between – 4 and 5 -4, ____, 5 The two arithmetic means are __ and __, since – 4, __, 5 forms an arithmetic sequence.

Find three arithmetic means between 1 and 4 1, ____, 4 The three arithmetic means are ___, and ___ since 1, ___, 4 forms an arithmetic sequence.

Find three arithmetic means between 1 and 4 1, ____, 4 The three arithmetic means are ___, and ___ since 1, ___, 4 forms an arithmetic sequence.

Find n for the series in which __ __ __

Find n for the series in which __ __ __

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